Apparatus for interferometric measurement of displacements

ABSTRACT

An apparatus for interferometric measurement of displacements wherein two interferometers each with a movable mirror which are mounted on a carriage in perpendicularly intersecting relationship indicate the displacements of the carriage along the X and Y axes in the number of interference fringes passing a certain point in an interference field of view; the number of interference fringes appearing in the interference field of view of the interferometer is counted by a counter and converted to the value of displacements by an arithmetic calculator; the yawing displacements of the carriage are determined by detecting phase differece between electrcal signals obtained by photoelectrical conversion from different points in the interference field of view; and the signals thus produced actuate a servo mechanism to correct the determined yawing displacements.

1451 Mar. 12, 1974 1 APPARATUS FOR INTERFEROMETRIC MEASUREMENT OFDISPLACEMENTS [75] Inventor: Hitoshi Takabayashi, Saitama,

Japan [73] Assignee: Anritsu Electric Co., Ltd., Tokyo,

Japan [22] Filed: Nov. 29, 19 71 21 Appl. No.: 202,768

[30] Foreign Application Priority Data Nov. 30 1970 Japan 45-105013 July14, 1971 Japan... 46-51750 -July 15, 1971 Japan 46-61622[U] 52- Us. c1.356/106 R, 356/110 51 1m. (:1. G01b 9/02 [58] Field ofSearch 356/106,107, 108, 109, 356/110, 111, 112, 113

[56] References Cited UNITED STATES PATENTS 3,692,413 9/1972 Marcy et al356/110 3,527,537 9/1970- Hobrough 356/110 PHASE DIFFERENCE DETECTORPrimary Examiner-Ronald L. Wibert Assistant Examiner-Conrad ClarkAttorney, Agerit, or Firm-K.emon, Palmer & Estabrook [57] ABSTRACT Anapparatus for interferometric measurement of displacements wherein t wointerferometers each with a movable mirror which are mounted on acarriage in perpendicularly intersecting relationship indicate thedisplacements of the carriage along the X and Y axes in the number ofinterference fringes passing a certain point in an interference field ofview; the number of interference fringes appearing in the interferencefield of view of the interferometer is counted by a counter andconverted to the value of displacements by an arithmetic calculator; theyawing displacements of the carriage are determined by detecting phasedifferece between electrcal signals obtained by photoelectricalconversion from different points in the interference field of view; andthe signals thus produced actuate a servo mechanism to correct thedetermined yawing displacements.

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APPARATUS FOR INTERFEROMETRIC MEASUREMENT OF DISPLACEMENTS BACKGROUND OFTHE INVENTION This invention relates to an apparatus for interferometicmeasurement of displacements and more particularly to such apparatus formeasuring multidimensional displacernents.

The prior art interferometric measuring apparatus includes a pair ofinterferometer each comprising a reference mirror, half mirror andmovable mirror fitted to the carriage and disposed in perpendicularlyintersect ing relationship, thereby counting the number of interferencefringes passing a certain point in an interference field when thecarriage is moved along the X and Y axes so as to measure the extent ofsaid movements. This apparatus has a common source of light for a pairof interferometers. Since the half and reference mirrors are fixed inthe same plane, the two-dimensional displacements of the movable mirrorcan be determined by these stationary units. However, such conventionalapparatus has the drawback that the carriage is likely to presentrotations A6 due to the mechanical inaccuracy of a carriage feeder.

Further, the measurement of the moved length of the carriage by means ofthe interferometer is effected by counting the changing numbers ofinterference fringes in an interference field of view. The frequencywhich interference fringes pass a certain point amounts to about 70Hzeven in the case where the carriage is moved at a slow rate namely of 1mm/min. Said frequency generally ranges fromzero to about I00 KHz.Accordingly, the number of interference fringes is counted by acombination of photoelectric and electric measurements.-

Ide ntification of the direction in which the carriage travels requirestwo periodic signals having different phases. These signals consist oftwo sinusoidal signals each drawn out from two different places in theinterference field of view to represent the displacements of the movablemirror. If, in this case, said two signals are drawn out from adjacentplaces in the interference field of view, then changes in the phasedifference of the signals resulting from the-rotating displacements orrotating deviation of the carriage can be reduced, thus enabling thestable counting of interference fringes. Since, however, the prior artapparatus cannot determine the rotating displacements of the carriage,the measured values are subject to errors; The errors resulting fromsaid rotating displacements are known as the Abbe errors which definethe limit of determination.

Therefore, to remodel the conventional apparatus into a type capable ofdisplaying the same degres of measurement accuracy as the generallyobtained interferometric sensitivity which should be sufficient toindicate 0.3 to 0.02 microns of the moved length of the carriage, thereis no other available method than machining the carriage feedingmechanism of said apparatus with superhigh precision. However, thisoperation practically presents extremely great difficulties.

A device for correcting the measured movement of the carriage bygenerating signals to detect rotating displacements resulting from saidmovement and actuating a servo mechanism according to said detectedsignals is already'disclosed in Ruling of Large Diffraction Gratingswith Interferometric Control, .lournal of the Optical Society ofAmerica, Vol. 47, pp 15 to 22, 7.

However, this device is primarily intended for unidimensionalmeasurements. It consists in feeding the carriage at a constant rate,detecting electric signals having a certain frequency from the movementof interference fringes at a constant speed, comparing the phase of thedetected signals with that of a reference signal using an ordinaryphasedifference measuring device or detector hereafter called phasedifference detector thereby determining phase differences between thesetwo types of signals. For such device, however, the carriage should bemoved at an extremely constant rate, presenting considerably technicaldifficulties in application to multidimensional measurements ofdisplacements with variable carriage velocity.

SUMMARY OF THE INVENTION.

This invention is intended to provide an apparatus for interferometricmeasurement of displacements which consists in detecting the rotatingdisplacements or rotating deviations of the movable mirror, carrying outcorrections according to the detected signals from the interferometermechanically or electrically in order to elevate measurement accuracy.

According this invention, there are provided two perpendicularlyintersectinginterferometers each including movable mirrors fitted to acarriage. In the interference field of view of each unit, are disposedphotoelectric converters, output signal from which are supplied to acounter and phase difference detector. The counter counts the number ofinterference fringes passing a certain point in the interference fieldof view. The phase difference detector determines the angle of thecarriage rotation. Signals obtained by said phase difference detectorare used mechanically to correct the detected rotating angle through acontrol device.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram of aninterferometric displacement measuring apparatus according to anembodiment of this invention;

FIG. 2 is a perspective view of the carriage of the apparatus of FIG. 1;

FIG. 3 is a side view of the carriage of FIG. 2;

FIG. 4 is a top view of the movable base of the carriage of FIG. 2;

FIG. 5 is a perspective view of the carriage of FIG.

2.to which there is added a mechanism for correcting the pitchingdisplacements of the carriage of FIG. 2;

FIG. 6 is a top view of a carriage according to another embodiment ofthe invention which is provided with a modification of said pitchingdisplacement correcting mechanism;

FIG. 7 is a side view of the carriage of FIG. 6;'

FIG. 8 is a top view of the carriage according to still anotherembodiment of the invention provided with 'a modification of saidpitching displacement correcting mechanism;

FIG. 9 is a side view of the carriage of FIG. 8;

FIG. 10 is an elevation of a movable mirror used in the apparatus of FIG. 1;

FIG. 11 is a back view of the movable mirror of FIG.

FIG. 12 is a side sectional view of the movable mirror of FIG. 10;

FIG. 13 illustrates the manner in which the movable mirror of FIG. isadjusted;

FIG. 14 presents the principle whereby the interferometer is operated;

FIG. 15 shows interference fringes appearing on the screen of theinterferometer;

FIG. 16 is an enlarged view of the interference fringes of FIG. 15;

FIG. 17 is a block circuit diagram of a phase difference detector usedin the interferometric displacement measuring apparatus of theinvention;

FIGS. 18A, 18B, 18C and 18D indicate the wave forms ofsignals generatedfrom the various parts of the phase differnce detector of FIG. 17;

FIG. 19 gives characteristics of the phase difference detector of FIG.17;

FIG. 20 is a block circuit diagram of an interferometric displacementmeasuring apparatus according to i metric displacement measuringapparatus according to a still further embodiment of the invention wherethe measured movement of said carriage is corrected by the thermalexpansion ofa metal wire used in a correction device;

FIG. 24 is a perspective view of the correction device used in theapparatus of FIG. 23; and

FIG. 25 is a perspective view of another type of correction device.

DETAILED DESCRIPTION OF THE INVENTION There will now be described byreference to FIGS. 1 to 19 an interferometric displacement measuringapparatus. Referring to FIG. 1, a beam from a source of monochromaticlight 31 is separated into two parts by a half mirror 32. The dividedparts proceed to other half mirrors 33 and 34, by which they are furtherdivided into two parts. They are conducted to fixed reference mirrors35.and 36 and movable plane mirrors 38 and 39 fitted to the adjacentsides of a carriage 37. The light beams reflected by the referencemirrors 35 and 36 and movable plane mirrors 38 and 39 are returned tothe aforesaid half mirrors 33 and 34. The light beams interfered by eachother on the half mirrors are detected by photoelectric converters 40and 41 disposed at two specified places to be converted to electricsignals. Output signals from said photoelectric converters 40 and 41 arecounted by counters 42 and 43. The results of counting by said counters42 and 43 are operated by an arithmetic unit to indicate the amounts ofdisplacement in the form converted to units of length. The two sets ofelectric signals obtained from the photoelectric converters 40 and 41are conducted to the corresponding phase difference detectors 45 and 46.The rotating displacements of the carriage are determined from changesin a phase difference between said electrical signals in each set. Aphase difference detector to be employed for detecting from such signalsthe variation of the phase difference is able to function despite thecarriage which moves at an ever changing speed and respond to a slightshock or vibration of the carriage. Detected outputs from said detectors45 and 46 are added together to be amplified by an adder amplifier 47and then conducted to a servo motor 48 which is consequently put intooperation to actuate a potentiometer 49. Output from said potentiometer49 and that from the adder amplifier 47 are added together to beamplified by an amplifier 50 and supplied to a servo actuator 51 fittedto the carriage 37 for its energization, thereby to correct the rotatingdisplacements of the latter.

The carriage 37 includes, as illustrated in FIG. 2, four support pillars53 of elastic material erected on a carriage base 52 and a carriageplate 54 mounted on said support pillars 53. To the edges of twoadjacent sides of the carriage plate 54 are fitted the movable mirrors38 and 39. Another servo motor 55 (FIG. 4) is fixed on said carriage 52.The shaft of said servo motor 55 is mechanically connected to a leadscrew 56 for its rotation which is engaged by a screw-threaded nut 57.This nut 57 travels in the axial direction of the lead screw along theguide members58 and 59 disposed on both sides of said nut 57. To one endof the nut 57 is connected one end of a wire 60, the other end of whichis fastened to a projection 62 (FIG. 3) disposed on the underside of thecarriage plate 54 through guide reels 61a, 61b, 61c and 61d. To theother end of the nut 57 is connected one end of a wire 63, the other endof which is connected through guide reels 64a, 64band 64c to aprojection 65 (FIG. 3) similarly disposed on the underside of thecarriage plate 54 opposite to the aforementioned projection 62.

There will now be described the operation of the carriage 37 arranged asdescribed above. First, the servo motor 48 is driven to adjust outputfrom the potentiometer 49 and the output torque of the other servo motor55 is so varied as to reduce a sum of outputs from the phase differencedetectors 45 and 46 to zero. When, under this condition, the carriagebase 52 travels, it presents rotating displacement due to errors inmachining its guide surface, causing the carriage plate 54 fitted withthe movable mirrors 38 and 39 to indicate the corresponding rotatingdisplacements. As the result of the rotating displacements of thecarriage plate 54, there is produced positive or negative output fromthe phase difference detectors 45 and 46 according to the dire-ction inwhich said carriage plate 54 rotates. Outputs from said detectors 45 and46 actuate the servo motor 48 to increase or decrease output from thepotentiometer 49. Outputs from the potentiometer and adder amplifier 47are conducted to drive the servo motor 55 included in the servo'actuator51. The drive of said servo motor 55 leads to the rotation of the leadscrew 56 and the forward movement of the nut 57. The nut 57 supplies byits travel the projections 62 and 65 formed on the underside of thecarriage plate 54 with forces acting in opposite directions in ahorizontal plane through the wires 60 and 63. Accordingly, the carriageplate 54 is subject to coupled forces of rotation corresponding to therotation of the carriage base 52 and acting against the elasticrestoring forces of the support pillars 53. The magnitude of saidcoupled forces varies with outputs from the adder amplifier 47 andpotentiometer 49, thereby causing the carriage plate 54 to rotate incorresponding relationship to the movement of the carriage base 52. Therotation of the carriage plate 54 is so controlled that the normals ofthe movable mirrors 38 and 39 fitted to said plate 54 are always alignedwith the initially set direction. Accordingly, the rotatingdisplacements of the carriage plate 54 resulting from the movementof thecarriage base 52 is con trolled with high precision, enabling said plate54 and moval mirrors 38 and 39 to move in very accurate parallelrelationship with the stationary members. Since the deviation of thecarriage plate 54 of the carriage 37 as a wholeis mechanicallycorrected, accurate measurement can be made without the necessity ofparticularly correcting the values counted by the counters 42 and 43.Experiments show that the aforesaid parallelism could be maintained at alevel of less than 0.1 are sec. This means that the difference ofdisplacements between two points on the carriage plate 54 200mm apartfrom each other indicated 200 X 0.1 X 5 X to 10 mm,that is, less than0.1 micron generally demanded of interferometric sensitivity. 1

The foregoing embodiment relates to the case where correction was madeof the displacements of the carriage 37 when it rotated around avertical axis. Actually, however, the carriage 37 also presentsdisplacements when it rotates around a horizontal axis, that is,

pitching displacements. The apparatus of this invention enables evencorrection of said pitching displacements.

Referring to FIG. 5, there are formed on the carriage plate 54 of thecarriage 37 projecting fitting pins 70a and 70b at the center of theforward and rear sides in the direction of x and similar projectingfitting pins 71a and 71b at the center of the forward and rear sides inthe direction of y. The head of said fitting pins 70a, 70b, 71a and 71bis connected to one end of each of the corresponding coil springs 72a,72b, 73a and 74b. The

other ends of said coil springs 72a, 72b, 73a and 74b are jointlyconnected to a fulcrum section 78 through the corresponding spring forceadjusters 74a, 74b, 75a and 75b formed into a hollow cylindrical shapeand connection wires 76a, 76b, and 77a and 77b. This arrangementsuspends the carriage plate 54 from the fulcrum section 78. The coilsprings 72 a, 72b; 73a and 73b normally urges the carriage 37 upward,and partially adjusts the pressure with which the carriage 37 as a wholeabuts against the guide surface of a separate member. The spring forceadjusters 74b, 74b, 75a and 75b adjust the effective length of the coilsprings 72a, 72b, 73a and 73b to vary their elastic constant, that is,their upward acting tensile force relative to their elongation.Adjustment of the force of said springs 72a, 72b, 73a and 73b iseffected by forcing an engagement pin 80 into one of insertion parts 79formed in the peripheral wall of the hollow cylindrical adjusters 74a,74b, 75a and 75b so as to catch the desired part of the upper endportion of the coil springs 72a, 72b, 73a and 73b pulled into saidadjusters.

There will now be described the operation of a mechanism for correctingthe aforesaid pitching displacements of the carriage 37. For example,where the carriage base 52 is guided to the left in the direction of x,

then the fitting pin 70a fixed on the forward side of the carriage plate54 as viewed in the travelling direction of the carriage base 52' isspaced further apart from the fulcrum section 78, whereas the fittingpin 70b disposed on the rear side of the carriage plate 54 drawn nearerto the fulcrum section 78. As apparent from this fact, the varyingdistances between the fulcrum section 78 and said two fitting pins 70aand 70b, that is,

changes in the forces acting on the fulcrum section 78 constitute aquadratic function of the moved length of the carriage 37. As a rule,the center of gravity of the carriage 37 is shifted in the direction inwhich the carriage 37 slides over the guide surface of a separatemember, with the result that the carriage exhibits very fine pitchingdisplacements. Since, according to'the experiment, the angle of saidpitching is proportional to the shifting of the center of gravity thevertical. movement of the fitting pins a and 70b together with thecarriage 37 constitutes a quadratic function of the pins travel in thedirections of x and y. When the carriage .37 moves to the left as viewedfrom FIG. 5, the fulcrum section 78 receives the varying forces of thecoil springs 72a and 72b. The aforesaid vertical movement of the forwardand rear fitting pins 700 and 70b is counterbalanced by said varyingforces, that is, correction forces. If, therefore, the elasticconstantof the coil springs 72a and 72b, or the distance between thefitting pins 70a and 70b themselves is so chosen in advance as to attainthe abovementioned counterbalancing effect, then the carriage 37 cantravel without any pitching displacement at all. This holds true withthe movement of the carriage 37 in any other directions than to theindicated leftside.

There will now be described by reference to FIGS. 6 and 7 another devicefor correcting the pitching displacements of the carriage 37. Thecarriage 37 is so disposed as to move, for example, to the indicatedleft and right sides over a guide 86 by being carried on guide rollers85. To both sides of the indicated left and right end portions of theguide board 86 are attached fitting plates 87 horizontally projectingfrom said left and right end portions. To the outer ends of the fittingplates 87 are fixed support rods 88a, 88b, 89a and 89b substantially atright angles. In the lower part of the support rod is formed avertically elongated sliding slit 90. To the fitting plate 87 isconnected by thread engagement an operating screw, 91 through thesliding hole 90. This operating screw 91 is normally fixed and onlyloosened when the support rod is made to slide vertically foradjustment, and again tightened when brought to the desired position. Toboth sides of the carriage 37 are fitted pulleys 92a, 92b, 93a and 93btwo on each side through fitting arms 98a, 98b, 99a and 99b. Between thesupport rods 88a amd 89a as well as between the support rods 88b and 89bmutually facing in the travelling direction of the carriage 37 arestretched wires 94a and .9412 respectively. These wires 94a and 94bupwardly support the carriage 37 through the pulleys 92a, 92b, 93a and93b. Accordingly, the pulleys 92a, 92b, 93a and 93b roll on the wires94a and 94b when the carriage 37 travels. The tension of the wires 94aand 94b is controlled by adjusting adjusters 95a and 95b fitted to thesupport rods 89a and 8912 which consist of nuts 96a and 96b and screws97a and 97b engaged therewith.

There will now be described the operation of a pitch ing displacementcorrecting device arranged as dc scribed above. When the carriage 37 islocated at the center of the guide board 86, those portions of the wires94a and 94b which are defined between the pulleys 92a and 93a as well asbetween. the pulleys 92b and 93b sag to a maximum extent, the extent ofsaid sagging being progressively reduced as the carriage 37 is furthermoved, for example, to the indicated left side. As the result of saidmovement of the carriage 37, the

force of the wires 94a and 94b acting on the forward pulleys 92a and92b. gradually increase, whereas the force of said wires 94a and 94bacting on the rear pulleys 93a and 93b progressively decrease. Theseautomatically varying forces of the wires 94a and 94b of correctionforces constitute a quadratic function of the moved length of thecarriage 37. If, therefore, the tension of the wires 94a and 94b and theheight of the support pillars 88a, 88b, 89a and 89b are properly chosenin advance, the carriage 37 can move without any ptiching displacement.

The foregoing description of the pitching displacement correcting deviceillustrated in FIGS. 6 and 7 relates to the case where the carriage 37was made to move in a unidimensional direction. However, a combinationof two such devices having the same arrangement enables the carriage 37to travel in bidimensional directions without pitching displacements.

There will now be described by reference to FIGS. 8

and 9 a third device for correcting pitching displacements. To bothsides of the forward and rear end portions of the carriage 37 in itstravelling direction are projectively fixed fitting arm assemblies 100a,10012 and 101b each of which consists of a pair of unit arms disposedone on the other. To the outer end ofthe respective arm assemblies arerotatablly fitted a pair of rollers 103. On both sides of the carriage37 in its travelling direction are disposed ribbon-shaped plate springs102a and 102b, which are each held between said pair of rollers 103. Theribbon-shaped plate springs 102a and 10212 are formed into a prescribed'curved shape and maintained at various heights as measured from theupper surface of a support table 104 which represent the expectedpitching displacements of the carriage 37 during its travel. The variousheights of the curved portion of the plate spring can be adjusted bychanging the height of the support rods 105 penetrating said supporttable 104. According to the pitching displacement correcting deviceshown in FIGS. 8 and 9, where the carriage 37 is supposed to present apitching displacement in a counterclockwise direction as viewed fromFIG. 9 when it is brought to a certain place on a separate guide plateor passes said place, that part of the curved plate spring whichrepresents the extent of said expected pitching displacement ispreviously chosen to have a relatively great height. Conversely wherethe pitching displacement tends to take place in a clockwise direction,the aforesaid part of the curved plate spring is set in advance at arelatively low level.

There will now be described the operation of the pitching displacementcorrecting device of FIGS. 8 and 9. When, as the result of the movementof the carriage 37, the forward paired rollers 103 fixed to the fittingarms 95a and 95b clamp those parts of the plate springs 102a and l02bwhich are previously chosen to have a relatively great height, then theend of the elastic fitting 2 arm assemblies 100a and 100b is elasticallycurved upward to supply the carriage 37 with a reaction proportional tosaid deformation, thereby counterbalancing a pitching displacementoccurring therein. As described above, the fitting arm assemblies 100a,100b, 1010 and llb are subject to an elastic reaction according to thecurvature of the plate springs 102a and 102b as the result of the travelof the carriage 37. If, therefore, previous determination is made of theextent of the pitching displacement of the carriage 37 at a given pointand the placements of the carriage 37 are offset by the'co'rrectionforce derived from the curved form of the plate springs 102a and 10212,enabling the carriage 37 to move without any pitching displacement.

There will now be described the movable mirrors 38 and 39 fitted to thecarriage 37. Said movable mirrors 38 and 39 are generally of a typehaving good optical flatness. While a mirror may be lapped to obtain asatisfactory flatness, the undermentioned process facilitatesmanufacture.

A plate-like material, for example, a plane mirror under a normalcondition is supposed to give rise to deformation by three kinds ofassumed external forces, that is, (i) a distributed moment, (ii) ashearing force both acting on the edge of the plate and (iii) a pressureapplied to the central part of the plate. Now let deviations of theflatness of the plate from the ideal flatness at various points thereonunder normal condition be designated as w(x, y). The forces supposed toproduce the aforesaid deviations w consist of a moment M(n, t), ashearing force Q(n, t) acting on the edge of the plate and a pressureP(x, y) perpendicularly acting on the surface thereof. The characters nand t represent the normal and the tangential direction at the edge ofthe plate respectively.

Substituting w in the known differential equation representing thedeflection of the plate as a value of said deflection, then theassociated pressure P(x, y) is determined.

where: g

D the flexural rigidity of the plate The values of M(n, t) and Q(n, t)are determined from the following equations.

If, therefore, there are applied to the plate a pressure P(x, y), momentM(n, t) and shearing force Q(n, t) representing the values reversed fromthose indicated by the aforementioned external forces used in theequations l (2) and (3) above,-then the deviations W(x, y) arecounterbalanced, enabling the surface of the plate to have an ideal flatplane.

The movable mirror is manufactured on the basis of the above-mentionedtheory. Referring to FIGS. 10 to 12, there is pressed a thin rectangularsheet 1 12 against the central part of the backside of a rectangularplane mirror 110. Around said thin sheet 112 are disposed thinrectangular rings 113 and 114 coaxially at a prescribed interval. To thebackside of the mirror is further fitted a rectangular elastic substrate115. Around the front periphery of the mirror are attached thinrectangular rings 116 and 117 coaxially at a prescribed interval. On thefront edge of the mirror 110 is mounted a rectangular ring-shapedelastic keep plate 118. Outside of the entire periphery of the mirror110 are disposed a plurality of pipes 119 of equal length at aprescribed space so as to bridge the substrate 115and keep plate 118.The substrate 115, pipes 119 and keep plate 118 are penetrated by a bolt120, with the exposed end of which there is engaged a nut 121 to fixthem jointly.

The substrate 115 and keep plate 118 are bored with a plurality of screwholesinto which there are fitted adjustment screws 122, the inner end ofwhich is pressed against the mirror 110 through the thin sheet 112, andthin rings 113, 114, 116 and 117. When, under this condition, theadjustment screws 112a and 122b are so turned as to cause their ends topress the mirror 110 in the directions of the indicated arrows a and brespectively, then the mirror 110 receives a moment acting in thedirection of the indicated arrow M. Where adjustment screws 122c and122d are tuned the mirror 110 receives an opposite moment to thepreceding case. When there is applied pressure to the mirror 110 byturning the mutually facing paired adjustment screws 122, there isobtained a required moment. When these adjustment screws are workedindividually there results a shearing force. When there are turned theadjustment screws 122 on the periphery of the mirror 110 there isapplied pressure to said section. When there are worked the adjustmentscrews 122 fitted to the central part of the substrate 115, there isapplied pressure to said section. When, therefore, adjustment isconducted by operating a proper combination of the adjustment screws122, it is possible to eliminate the residual deformation of the mirror110, enabling it to have an ideal or approximately ideal plane.

It is advisable to carry out the aforesaid adjustment by disposing, asillustrated in, for example, FIG. 13, a standard transparent plane plate123 ahead of-a plane mirror 110 being adjusted in parallel relationship,10-

cating a half mirror 124 slantwise facing said transparent plate 123,projecting parallel beams of light 125 through said half mirror 124 atright angles to said transparent plate 123 and while observinginterference fringes 126 through said half mirror 124, properly workingthe adjustment screws l22 so as to eliminate the curvature of saidinterference fringes 126. This process of adjustment easily reducesirregularities on the surface of the mirror 110 to less than one-tenthof those originally occurring thereon. A ground plane mirror generallyhas such a flatness as can be indicated by about one interference fringeor a single wave length. If a plane mirror thus ground is constructed asillustrated in FIG. 12, then it can be made always to display anextremely even plane whose flatness amounts to less than )t/lO, that is,one-tenth of a single wave length.

There will now be described a phase difference measuring device. Beforereferring thereto, however, there will be explained the generation ofinterference fringes.

presents an inclination, though extremely small, while 1= 2 {l cos[(21r/a) u (41171)} where:

a interval of interference fringes as measured in the direction of u l Awavelength of monochromatic light 132 used x movement of the mirror 130It will be noted that the above equation relates to the case where theposition taken by the mirror when the dark lines of interference fringespass a point of u 0 is considered as the base of its movement. Theseinterference fringes constitute a sinusoidal function of the movement ofthe carriage and, where the mirror included in the interferometer has asatisfactory flatness, can also be used as a sinusoidal function of agiven point in the interferencefield of view. Let it be assumed thatinterference fringes were observed at points 14,, 11 Then there aregenerated light signals expressed by the following equations.

1 1,, {1+ sin 477m an 1 I0{1+ Sin (47r/Ax 8 I3 10+ Sin 'l' (5) 1f theangle between the virtual image 1 33 of the reference mirror and themirror 130 is represented by 6, then there results the knownrelationship d0 M2. That is, d varies with 6. With, therefore, 8, takenas the base in the equation (5), a difference between 8, and '6 and thatbetween 6 and 8 also change. Conversely, variations in 0 can bedetermined from changes in said differences.

The aforementioned interferometric apparatus determines 6 in thefollowing manner. There are perforated, as shown in FIG. 16, four pinholes A, B, C and D on the abscissa axis u of an interference field ofview 131. From these pin holes A, B, C and D are drawn out lightsignals. Said pin holes are located in the following relationship.

Where d represents a distance between the central parts of interferencefringes appearing in parallel at a certain inclination to the centralline of the interference field of view; FIG; 16 indicates the brightnessof interference fringes in the density of horizontal lines. With sucharrangement, there are drawn out from the aforesaid pin holes lightsignals which may by expressed by the following equation- While 8 givenin the above equation (6) has a smaller value than 21r, it of coursevaries if the inclination of the mirror image 133' to the mirror 130changes (FIG. 14).

Light signals appearing at the aforementioned pin holes A, B, C and Dare converted, as shown FIG. 17, into electrical signals by photo-cell135 to 138, outputs from which may respectively be expressed by thefollowing equations.

The above outputs have a frequency proportional to the moving speed ofthe mirror and generally indicating about 30 KHz for the moving speed ofmm/sec. Of said outputs, those which become equal in every respect whenthe phase difference 8 is reduced to zero, that is, a group of 1, 1 anda group of 1 1 are supplied to differential amplifiers 139 and 140respectively. Outputs 1, and I from these differential amplifiers 139and 140 respectively may be expressed by the following equations.

On the other hand, substantially stable light signals IS and which areproportional to the intensity of a light source are converted into D. C.electrical signals 1 and 1 by other photo-cell 141 and 142. Theseelectrical signals 1 1 may respectively be expressed by the followingequations.

I, l 1/ V2 The D.C. signal I is conducted to comparators 143 and 146together with output signals I and-1 from the photoelectric converters136 and 137, whereas the D.C. signal is supplied to comparators 144 and145 together with output signals 1, and 1, from the photocell 135 and138. Outputs I 1 I and 1 from said comparators 143 to 146 mayrespectively be expressed by the following equations.

In case of cos[(41r/)t)x 8] l/ V2 0 1 =1 In case of cos [(41r/A)x 61+ 1/V2 0 I =1 In case of sin [(41r/A)x 46] l/ V2 0 I =1 In case of sin 41%46 1N2 0 1,, 1

In other cases, said outputs 1 to 1 are so controlled as to indicatezero. Output 1 from the differential amplifier 139 and output I, fromthe comparator 144 are supplied to a gate 147, while output 1 from thedifferential amplifier 140 and output 1 from the comparator 145 areconducted to a gate 148. A gate 149 is supplied through an inverter 151with output 1 from the differential amplifier 13 9 and output 1 from thecomparator 143, while a gate is sup- {cos x 58) cos x 6)} dx 1: A A if)a An average output from the adder 153 is determined simply bydividingthe value of the above equation l l) by the integral interval)t/2.

1, 4 \/2/1r sin 28 cos 8 FIG. 18A indicates for comparison the waveforms of inputs I and I to the comparator 139 and that of the othersignal I FIG. 18B shows the wave form of output 1 from the differentialamplifier 139 and those of inputs 1 and 1 to the comparator 144.

Output from the comparator 144 controls the signal 1 at the gate 147.FIG. 18C indicates the wave form of output from the gate 148. FIG. 18Dpresents the wave form of a composite signal obtained by summing upoutputs from the gates 147 to 150. FIG. 19 gives a value derived fromthe above equation (12). As seen from FIG. 19, there is obtained amaximum output when the phase difference indicates about 35. In case of11/2 8 1r/2 the output is rendered positive or negative according as thephase difference becomes positive or negative. In case of I81 1r/ l2 theoutput is substantially proportional to the phase difference.

There will now be discussed the phase difference detector in theaforementioned manner in connection with the rotating angle of a mirror.The phase difference detector can carry out detection at least when themirror is inclined through a phase angle of less than 1. Further, let itbe assumed that two A and B in an interference field of view at whichthere are drawn out light signals 1,, and 1 having a phase difference of8 are spaced 5 mm from each other and that part of the mirrorcorresponding to said space of 5 mm is moved with an error fallingwithin the range of H360 X M2. Then the phase difference can bedetected. When converted l/ X M2 X 360= 1.7 X (rad) or 0.03 arc sec.

This value far exceeds the sensitivity of an angle gauge such as anautocollimator which has heretofore been used in determining minuterotations.

When conducted through a low pass filter, output from the adder 153 canbe substantially converted to DC current. When said output has a stilllower frequency or a frequency falling within the DC. range, then thereis obtained a signal having such a wave form as shown in FIG. 18D. Thisoutput signal has a blind sector X and another sector Y where there isobtained a value twice the average value of outputs of the adder 153.Particularly where an object (the reference mirror 133) stands at rest,there possibly result determination errors. If the mirror is subjectedto slight external vibrations corresponding to a fraction of the wavelength of light, there can be obtained an average value of theaforementioned output from the adder 153. If, otherwise, the referencemirror 133 is under a stable rest position free from any such externalvibrations, it is only required purposely to wave the mirror 135slightly back andforth for vibrations in order to determine said averagevalue. The more reduced the phase difference, the narrower the blindsector X and the Y sector where there is obtained a value twice that ofthe X sector. This means that smaller phase differences all the moreminimize errors. Accordingly, the phase difference detector of thisinvention is most effective to determine extremely minute phasedifferences. Further, even when the reference mirror moves in theopposite direction, output from the adder 153 will not vary, providedthe mirrors constituting an interferometer make a prescribed relativeinclination. This is ascertained from the fact that the results arrivedat by exchanging the upper limit of integration given in the equation (1l) for the lower limit thereof to substitute a'x by dx are exactly thesame as those obtained before such substitution.

The aforesaid phase fifference detector used light signals 1 1 l and 1However, this invention is not limited thereto, but permits variousmodifications thereof Because of I 1,, 2 I COS(-41T/)UC 26) sin 6, thedifference signal is in the same phase as 1 When, therefore, 1 is usedin controlling the gate, there is ob- .tained, unlike the precedingcase, an output proportional to sin 25, as naturally expected. To sumup, there are generated a plurality of first signals synchronizing withsecond two signals to be measured phase difference therebetween. Thefirst signals have phases different from the second two signals by thetotal amount of an integral multiple and mr/2 of the phase difference ofthe amount of either the integral multiple or n1r/2 thereof. There areselected two prescribed signals from among the plural first signals. Thetwo first signals are supplied to the differential amplifier to take outthedif ference therebetween.

The phase difference detector of this invention is also applicable toall determinations based on detection by synchronization signals, forexample, the measurement of the moved length of a carriage using theMoire fringes of an optical grid or a magnetic scale.

There will now be described the second to fourthembodiments of anapparatus for interferometric measurement of displacements. The parts ofthese embodiments the same as those of the first embodiment are denotedby the same numerals and description thereof is omitted. SecondEmbodiment This embodiment mechanically corrects the travel of themovable mirrors fitted to the carriage 37 and detects the correctedvalues. As shown in FIG. 20, outputs fromthe phase difference detectors45 and 46 are supplied to servo motors 48a and 48b respectively, whichdrive potentiometers 49a and 49b. Outputs from the potentiometers 49aand 49b are conducted to current amplifiers 67 and 68 respectivelytogether with outputs from the phase difference detectors45 and 46.

Outputs from the current amplifiers 67 and 68 energize the servoactuators and 161 fitted to the movable mirrors 38 and 39. Outputs fromsaid current amplifiers 67 and 68 are also summed up by an adder 162 andsupplied to an operation device 44 together with outputs from thecounters 42 and 43. The displacement of the carriage 37 computed by thecounters 42 and 43 is corrected by output from said'adder 162, enablingthe operation device 44 to figure out thetrue displacement of thecarriage 37. i

The ends on one side-of the two movable mirrors 38 and 39 which aredrawn near to eachv other are held between a plate spring 163 and afulcrum 165 and be tween a plate spring 164 and a fulcrum 166respectively. The ends on the other side of the movable mirrors 38 and39 are held between a plate spring 167 and the operable end amagnetostrictive element 169 included in a servo actuator 160 andbetween a plate spring 168 and the operable end of a magnetostrictiveelement included in a servo actuator 161 respectively. Themagnetostrictive elements 169 and 170 are wound with coils 171 and 172excited by outputs from the current amplifiers 67 and 68. Themagnetostrictive elements 169 and 170 consist of alloys of nickel with Iiron or copper. In this case it is preferred that said magnetostrictiveelements are thermally insulated from the coils 171 and 172 woundthereon and the outside.

If, in the aforementioned arrangement, bias current supplied to thecoils 171 and 172 is previously so set as to cause outputs from thephase difference detectors 45 and 46 to have a minimum value or to bereduced to zero, then the rotating displacement of the carriage 37resulting from its movement can be detected by the phase differencedetectors 45 and. 46. Detection outputs are amplified by the currentamplifiers 67 and 68 and supplied to the coils 171 and 172.

The magnetostrictive elements 169 and 170 vary in length according tothe energy of a magnetic feeld generated in the coils 171 and 172. Themovable mirrors 38 and 39 rotate about the fulcrums 165 and 166correspondingly to the movement of the carriage 37. Thus the normaldirection of the movable mirrors 38 and 39 can always be aligned withthe initially set direction. At this time, changes in outputs from thepotentiometers 49a and 49b are averaged by an adder 162, and determinedin the form of the minute rotating anglee A6 of the carriage 37.

The varying numbers of interference fringes appearing in aninterferometer provided with movable mirrors whose movement has thusbeen corrected can always be distinctly counted by the counters 42 and43. It will be noted that changes in the number of interference fringesrepresent the displacement of the movable mirrors 38 and 39 and not thatof the carriage 37 itself. The true displacement of the carriage 37 atgiven points X and Y is determined by the values obtained from thereversible counters 42 and 43, that is, on the basis on the coordinatethe axes X and Y and the rotating angle A0 of the carriage 37.

Since the movable mirrors 38 and 39 travel in parallel, the rotatingcenter of the movable mirror 38 relative to the carriage 37, that is,the true displacement (x y of the fulcrum 165 may be expressed asfollows.

Y+ (a/ \/2 A0 where;

a linear distance between the fulcrums 165 and It is assumed that thelinear direction is inclined 45 to the X and Y axes.

Now let it be assumed that with the fulcrum 165 taken as the origin, theprescribed points on the carriage 37 as plotted on coordinates aremeasured from said base in units of mm and said coordinates aredesignated as X and Y Since the carriage 37 as a whole has rotated onlythrough an angle of A0 and the displace ments of said points (on thecoordinates X and Y on the carriage 37 have already been determined, thetrue displacements (x, y) of said points (X Y may be expressed asfollows.

The second terms on the right side of the above equations representcorrected values. If said second term as a whole represents an effectivenumber consisting of two places, it will well serve the purpose.

Therefore, X Y a and A0 may have a rough value having errors of severalpercents. Operation for correction of such counter values and indicationof the displacement of the carriage 37 in metric units is performed bythe operatio device 44.

Third Embodiment Referring to FIG. 21, both ends of a reference mirror35 are held between piezoelectric quartz elements 175 and 176 fixed atone end so as to face the reference mirror 35 and springs 179 and 180.Both ends of a reference mirror 36 are held between piezoelectric quartzelements 179 and 180 and springs 181 and 182. Across both ends of eachof the piezoelectric quartz elements 175 and 176 is supplied voltagefrom a voltage amplifier 183, and across both ends of each of thepiezoelectric quartz elements 179 and 180 is impressed voltage from avoltage amplifier 184. When impressed with voltage, the aforementionedpiezoelectric elements present distortions in the direction in whichthere acts an electric field or at right angles to said direction Saidpiezoelectric distortions are generally so small as about 0.1 micron. Itis therefore preferred that the mutually facing piezoelectric elements175, 176, 177 and 178 be each formed into a small size and'so arrangedas to en able the reflectors 35 and 36 to rotate effectively by minutepiezoelectric distortions.

if, under the aforesaid arrangement, the piezoelectric elements 175,176, 177 and 178 are previously impressed with such bias voltage ascauses the phase difference detectors 45 and 46 to produce a minimumoutput, then the rotating or yawning displacement of the movable mirrors38 and 39 resulting from the movement of the carriage 37 can be detectedby said phase difference detectors 45 and 46. Detection outputstherefrom are amplified by the voltage amplifiers 183 and 184respectively, and conducted to the piezoelectric elements 175, 176, 177and 178. Said elements vary in size with the yawning displacement of themovable mirrors 38 and 39, causing the reference mirrors 35 and 36 tomake such a rotating displacement as realizes the constant inclinationof the movable mirrors to the images of the reference mirrors 35 and 36with respect to the half mirrors 33 and 34 respectively. Outputs fromthe potnetiometers 49a and 49b are averaged by being summed up by anadder 185. From the outputs of the adder 185 and counters 42 and 43 andthe other factors such as A8, X and Y can be determined, as in thesecond embodiment, the true displacement of the carriage 37.

There will now be described said determination in greater detail.Referring to FIG. 22, numerals 38 and 38H represent the positions of themovable mirror 38 before and after its'rotation, and numerals 35and 35Hthe positions of the reference mirror 35. In order to simplify thedescription, it is assumed that the normal of the surface of the movablemirror 38 and that of the reference mirror 35 are parallel to incominglight beams EF and EF respectively. An incident light beam L is dividedinto two fluxes, one of which is directed to the point F and the otherof which travels to the point F. The movement of a rigid bodyaccompanied with rotation may be deemed as a composition of itstranslation and its rotating displacement about a certain point. Here,the displacement of the movable mirror 38 is assumed to be a compositionof its translation in the X and Y axes and its rotation about anintersection 0 defined by an extension of the incident light EP in the Xaxis with an extension of an incident light (not shown) in the Y axis.The true value of said translation is immediately determined by acounter and the rotating displacement is determined from therelationship described below. An optical path difference before therotation of the movable mirror 38 may be expressed as 2(EF- EF') When,in case of EF 3F EF, two light beams separated at the point E after therotation of the movable mirror 38 are brought back to the half mirror 33by reflection, then do not converge at a single point, but are, asillustrated, located apart at the points G and G. A light beaminterfering with a light beam F'G is a light beam F "G' separated at thepoint E. This phenomenon is known as the shearing of light beams. Sincehow

1. An apparatus for interferometric measurement of displacements whichcomprises: a carriage; two interferometers each of wHich includes areference mirror, a half mirror and a movable mirror mounted on saidcarriage said interferometers arranged on axes which intersect at rightangles; two photoelectric converteres one associated respectively witheach of said interferometers and each having four photo-cells whichconvert four light signals appearing at four predetermined points in theinterference field of view of the corresponding interferometer to fourelectrical signals respectively; two counters one connected respectivelyto said photoelectric converters to count interference fringes passingthrough the interference field of view according to the electricalsignals from said photoelectric converter; two phase differencedetectors connected respectively to said photoelectric converters todetect variations of the phase differences between said electricalsignals from the corresponding photoelectric converter; and a correctiondevice for correcting for rotational deviations of said carriageaccording to outputs from said phase difference detectors.
 2. Anapparatus according to claim 1 wherein said correction device comprisesan adder amplifier connected to said phase difference detection forsumming up and amplifying the outputs therefrom; a servo motor connectedto be actuated by output from said adder-amplifier; a potentiometerdriven by said servomotor; a power amplifier connected to saidadder-amplifier and potentiometer for summing up and amplifying outputstherefrom; and a correction mechanism driven by the output from saidpower amplifier to correct for rotational deviation of said carriage. 3.An apparatus according to claim 2 wherein said carriage comprises acarriage base and a carriage plate fitted to said carriage base througha plurality of elastic members; and said correction mechanism comprisesa motor mounted on said carriage base and driven by the output from saidpower amplifier; a lead screw rotated by said motor; a nut reciprocatedby said lead screw; and means for causing minute rotations of saidcarriage according to the movement of said nut.
 4. An apparatusaccording to claim 1 wherein said correction device includes two controldevices coupled respectively to said phase difference detectors and eachdevice comprising a servo-motor connected to be actuated by the outputfrom said phase difference detector, a potentiometer driven by saidservomotor and a current amplifier for summing up and amplifying theoutputs from said potentiometer and said phase difference detector; anadder-amplifier connected to average the outputs from the potentiometersof said devices; two correction mechanisms mounted on the carriage andeach actuated according to output from the current amplifier to correctthe rotational deviation of said movable mirror so as to realize theconstant inclination of the movable mirror to the image of the referencemirror with respect to the half mirror; and an arithmetic unit toarithmetically correct the values of said counters in accordance withthe signal from said adder-amplifier obtained in response to therotational deviation of the carriage, thereby to detect an actualdisplacement of the carriage.
 5. An apparatus according to claim 4wherein each of said correction mechanisms includes means for pivotallyfitting one end of the movable mirrors to the carriage; and a platespring and magnetostrictive element for holding the other end of saidmirrors, said magnetostrictive element changing in size according tooutput current supplied thereto from the amplifier of said controldevice thereby giving a slight rotation to said movable mirror.
 6. Anapparatus according to claim 1 wherein said correction device includestwo control devices coupled respectively to said phase differencedetectors and each comprising a servo motor actuated by output from oneof said phase difference detectors, a potentiometer adjusted by saidservo-motor and a voltage amplifier for summing up and amplifyingoutputs from said potentiometer and said phase difference detector; acorrection mechanism actuated by output from the voltage amplifier ofsaid control device to pivot the reference mirror of the interferometerso as to realize the constant inclination of the reference mirror to theimage of the movable mirror with respect to the half mirror; and anarithmetic unit to arithmetically correct the values of said countersincluding errors caused in accordance with the deviation of thecarriage.
 7. An apparatus according to claim 6 wherein each of saidcorrection mechanisms comprises a pair of piezoelectric elementsdisposed in contact with both ends of the reference mirror of theinterferometer with the reference mirror arranged between thepiezoelectric elements each changing in size according to output voltagesupplied thereto from said voltage amplifier of said control device andgiving a slight rotation to said reference mirror.
 8. An apparatusaccording to claim 1 wherein said phase difference detector comprisestwo differential amplifiers each making a difference signal between twoprescribed signals selected from among the four signals from the fourphoto-cells; two inverters each changing the phase of the differencesignal by 180 degrees; four gates each allowing or obstructing thepassage of one of said difference signals from said differentialamplifiers or said inverted signals from said inverters; fourcomparators each of which makes a comparison between one of the foursignals from the photo-cells which substantially synchronize with saiddifference signals and one of two reference signals proportional to theintensity of a light source and which generates a signal to open one ofsaid gates when said difference signal or its inverted signal presents alarge amplitude; and an adder for summing up the difference signals andthe inverted signals which have passed through said gates.